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WWWJDIC lists いちにん and ににん as alternative readings of 一人 {ひとり} and 二人 {ふたり}, but I can't recall anywhere I heard those readings except when counting more than 10 people for example 三十一人 {さんじゅういちにん}. Is that the only situation where 一人 and 二人 are read as いちにん and ににん, or are there any other situations?

The only thing I can think of is 一人称【いちにんしょう】 and 二人称【ににんしょう】 meaning "first person" and "second person" respectively. This means "person" as in "point-of-view" or parts of speech ("third person" is 三人称【さんにんしょう】).